If anyone is travelling to Estonia, I can recommend the Elisa prepaid SIM. The starter pack costs €1 and comes with €1 credit. The maximum charge per day for unlimited Internet is €1.60, so I topped up with an additional €10, which should give enough for a week here for total €11. The card also does voice and text, should you require it. A single call, such as a top-up call activates the SIM.

The purchase was very simple - like Ireland - no ID required and no forms - just bought the pack and top-up in an Elisa shop. I think they are also available in kiosks etc. The APN is "internet" with no username or password. Coverage and speeds excellent around Tallinn so far.

I'm in Estonia now, and I have an Elisa prepaid SIM. I have not been able to get the data connection to work. I went to an Elisa shop at a mall today, and the people who worked there couldn't get it to work, either.

I looked up the settings on the internet, but none that I see make the phone
work. I have an AT&T Samsung Galaxy phone running Android ICS 4.0.

Update: After trying everything I could think of, I was never able to get a data connection with the Elisa SIM card. I don't know if this was some odd incompatibility with my phone or something else. I would advice anybody who wants to use Elisa to buy the 1 Euro card and make sure you have data before you pay for any recharges.

Update: After trying everything I could think of, I was never able to get a data connection with the Elisa SIM card. I don't know if this was some odd incompatibility with my phone or something else. I would advice anybody who wants to use Elisa to buy the 1 Euro card and make sure you have data before you pay for any recharges.

I was also using a Samsung Galaxy - with Android 2.3. Your phone has to be unlocked from your home network in order to use any foreign SIM. And you have to create a new APN in the Settings Menu - with the settings I gave in my first mail.

Settings>Mobile Networks>Access Point Names>New APN

The APN name for Elisa is "Internet", and no username or password is required. You need to make this your default APN while in Estonia.

There should be no problem, as long as your phone is unlocked. PM me if you have any difficulty.

It can be topped up with vouchers only, or if you have Estonian bank so you can topup with bank online, they don't accept payment with credit cards at all.

If roaming is active so it works outside of Estonia, valid for 6 months from last topup or activation moment.
You can topup with vouchers using USSD commands only
If you want I have vouchers to TELE2 and I should order new SIM cards after holidays (I work with TELE2)